Model-Oriented Data Analysis; Proceedings of an IIASA Workshop, Eisenach, GDR, March 9-13, 1987)

The main topics of this workshop were (1) optimal experimental design, (2) regression analysis, and (3) model testing and applications. Under the topic "Optimal experimental design" new optimality criteria based on asymptotic properties of relevant statistics were discussed. The use of additional restrictions on the designs were also discussed, inadequate and nonlinear models were considered and Bayesian approaches to the design problem in the nonlinear case were a focal point of the special session. It was emphasized that experimental design is a field of much current interest. During the sessions devoted to "Regression analysis" it became clear that there is an essential progress in statistics for nonlinear models. Here, besides the asymptotic behavior of several estimators the non-asymptotic properties of some interesting statistics were discussed. The distribution of the maximum-likelihood (ML) estimator in normal models and alternative estimators to the least-squares or ML estimators were discussed intensively. Several approaches to "resampling" were considered in connection with linear, nonlinear and semiparametric models. Some new results were reported concerning simulated likelihoods which provide a powerful tool for statistics in several types of models. The advantages and problems of bootstrapping, jackknifing and related methods were considered in a number of papers. Under the topic of "Model testing and applications" the papers covered a broad spectrum of problems. Methods for the detection of outliers and the consequences of transformations of data were discussed. Furthermore, robust regression methods, empirical Bayesian approaches and the stability of estimators were considered, together with numerical problems in data analysis and the use of computer packages

Semi-Supervised Single- and Multi-Domain Regression with Multi-Domain Training

We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of removing expressions from facial images and in the context of audio-visual word recognition, and provide comparisons to several recently proposed multi-modal learning algorithms.Comment: 24 pages, 6 figures, 2 table

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Pointwise adaptive estimation for robust and quantile regression

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is extended to image denoising and applied to CT scans in cancer research